Kant and Hume on Causality

Kant famously attempted to “answer” what he took to be
Hume's skeptical view of causality, most explicitly in the
Prolegomena to Any Future Metaphysics (1783); and, because
causality, for Kant, is a central example of a category or pure
concept of the understanding, his relationship to Hume on this topic
is central to his philosophy as a whole. Moreover, because Hume's
famous discussion of causality and induction is equally central to his
philosophy, understanding the relationship between the two
philosophers on this issue is crucial for a proper understanding of
modern philosophy more generally. Yet ever since Kant offered his
response to Hume the topic has been subject to intense
controversy. There is no consensus, of course, over whether Kant's
response succeeds, but there is no more consensus about what this
response is supposed to be. There has been sharp disagreement
concerning Kant's conception of causality, as well as Hume's, and,
accordingly, there has also been controversy over whether the two
conceptions really significantly differ. There has even been
disagreement concerning whether Hume's conception of causality and
induction is skeptical at all. We shall not discuss these
controversies in detail; rather, we shall concentrate on presenting
one particular perspective on this very complicated set of issues. We
shall clearly indicate, however, where especially controversial points
of interpretation arise and briefly describe some of the main
alternatives. (Most of this discussion will be confined to footnotes,
where we shall also present further, more specialized details.)

In the Preface to the Prolegomena Kant considers the supposed
science of metaphysics. He states that “no event has occurred
that could have been more decisive for the fate of this science than
the attack made upon it by David Hume” and goes on to say that
“Hume proceeded primarily from a single but important concept of
metaphysics, namely, that of the connection of cause and
effect” (4, 257; 7). (See the Bibliography for our method
of citation.) Over the next few pages Kant defends the importance of
Hume's “attack” on metaphysics against common-sense
opponents such as Thomas Reid, James Oswald, James Beattie, and Joseph
Priestley (all of whom, according to Kant, missed the point of Hume's
problem), and Kant then famously writes (4, 260; 10): “I freely
admit that it was the remembrance of David Hume which, many years ago,
first interrupted my dogmatic slumber and gave my investigations in
the field of speculative philosophy a completely different
direction.” Thus, it was Hume's “attack” on
metaphysics (and, in particular, on the concept of cause and effect)
which first provoked Kant himself to undertake a fundamental
reconsideration of this (supposed) science.

Later, in §§ 27–30 of the Prolegomena, Kant
returns to Hume's problem and presents his own solution. Kant begins,
in § 27, by stating that “here is now the place to remove
the Humean doubt from the ground up” (4, 310; 63); and he
continues, in § 29, by proposing “to make a trial with
Hume's problematic concept (his crux metaphysicorum),
namely the concept of cause” (4, 312; 65). Kant
concludes, in § 30, by stating that we are now in possession of
“a complete solution of the Humean problem” (4, 313;
66)—which, Kant adds, “rescues the a priori origin of the
pure concepts of the understanding and the validity of the general
laws of nature as laws of the understanding, in such a way that their
use is limited only to experience, because their possibility has its
ground merely in the relation of the understanding to experience,
however, not in such a way that they are derived from experience, but
that experience is derived from them, a completely reversed kind of
connection which never occurred to Hume” (ibid.).
Thus, Kant's “complete solution of the Humean problem”
directly involves him with his whole revolutionary theory of the
constitution of experience by the a priori concepts and principles of
the understanding—and with his revolutionary conception of
synthetic a priori judgments.

Indeed, when Kant first introduces Hume's problem in the Preface to
the Prolegomena he already indicates that the problem is
actually much more general, extending to all of the categories of the
understanding (4, 260; 10): “I thus first tried whether Hume's
objection might not be represented generally, and I soon found that
the concept of the connection of cause and effect is far from being
the only one by which the understanding thinks connections of things a
priori; rather, metaphysics consists wholly and completely of them. I
sought to secure their number, and since this succeeded as desired,
namely, from a single principle, I then proceeded to the deduction of
these concepts, on the basis of which I was now assured that they are
not derived from experience, as Hume had feared, but have sprung from
the pure understanding.”
Moreover, Kant soon explains, in § 5, how this more general
problem (common to all the categories and principles of the
understanding) is to be formulated: “How is cognition from pure
reason possible?” (4, 275; 27), or, more specifically,
“How are synthetic a priori propositions possible?” (4,
276; 28).

In the Introduction to the second (B) edition of the Critique of
Pure Reason (1787), Kant follows the Prolegomena in
formulating what he here calls “the general problem of pure
reason” (B19): “How are synthetic a priori judgments
possible?” And, as in the Prolegomena, Kant insists
that the possibility of metaphysics as a science entirely depends on
this problem (ibid.): “That metaphysics until now has remained
in such a wavering state of uncertainty and contradictions is to be
ascribed solely to the fact that this problem, and perhaps even the
distinction between analytic and synthetic
judgments, was not thought of earlier. Metaphysics stands or falls
with the solution of this problem, or on a satisfactory proof that the
possibility it requires to be explained does not in fact
obtain.”
Kant then immediately refers to “David Hume, who, among all
philosophers, came closest to this problem”; and he suggests,
once again, that Hume failed to perceive the solution because he did
not conceive the problem in its “[full] generality, but rather
stopped with the synthetic proposition of the connection of the effect
with the cause (principium causalitatis)” (ibid.).

It is only in the second edition of the Critique that Kant
gives such a prominent place to Hume and his “objection”
to causality, serving to introduce what Kant now calls “the
general problem of pure reason.” By contrast, the name of Hume
does not appear in either the Introduction or the Transcendental
Analytic in the first (A) edition (1781): it appears only in the
Transcendental Doctrine of Method at the very end of the book, in a
discussion of “skepticism” versus “dogmatism”
in metaphysics (where Hume's skepticism about causation, in
particular, is finally explicitly discussed). This is not to say, of
course, that implicit references to Hume are not found earlier in the
text of the first edition. Thus, for example, in a preliminary section
to the Transcendental Deduction Kant illustrates the need for such a
deduction with the concept of cause, and in both editions remarks
(A91/B124): “Appearances certainly provide cases from which a
rule is possible in accordance with which something usually happens,
but never that the succession is necessary; therefore, a
dignity pertains to the synthesis of cause and effect that cannot be
empirically expressed at all, namely, that the effect does not merely
follow upon the cause but is posited through it and follows
from it.”
But it is only in the second edition that Kant then goes on to mention
“David Hume” explicitly, as one who attempted to derive
the pure concepts of the understanding from experience (B127):
“namely, from a subjective necessity arising from frequent
association in experience—i.e., from custom—which
is subsequently falsely taken for objective.” This striking
difference between the two editions clearly reflects the importance of
the intervening appearance of the
Prolegomena.

Given the crucial importance of the Prolegomena in this
respect, it is natural to return to Kant's famous remarks in the
Preface to that work, where, as we have seen, Kant says that “it
was the remembrance of David Hume which, many years ago, first
interrupted my dogmatic slumber and gave my investigations in the
field of speculative philosophy a completely different
direction.” It is natural to wonder, in particular, about the
precise years to which Kant is referring and the specific events in
his intellectual development he has in mind. Here, however, we now
enter controversial terrain, where there are basically two competing
alternatives—both of which reflect the circumstance that Kant
could read Hume only in German translation.

Kant might be referring, on the one hand, to the late 1750s to mid
1760s. A translation of Hume's Enquiry Concerning Human
Understanding (originally published in 1748) appeared in 1755 and
was widely read in Germany. Kant had almost certainly read this
translation by the mid 1760s, by which time he himself expressed doubts
about whether causal connections could be known by reason alone and
even suggested that they were knowable only by experience. Or, on
the other hand, Kant might be referring to the mid 1770s. After
the Inaugural Dissertation appeared in 1770, Kant published
nothing more until the first edition of the Critique in
1781. Meanwhile, a German translation of Beattie's
Essay on the Nature and Immutability of Truth (originally
published in 1770) appeared in 1772, where, in particular, Beattie
quoted extensively from Book 1 of Hume's Treatise of Human
Nature (originally published in 1739). Thus, in the famous
“dogmatic slumber” passage, Kant might be referring either
to the mid 1760s, when he then had a “remembrance” of
reading the translation of Hume's Enquiry, or to the mid
1770s, when he then had a “remembrance” of reading
translations from the Treatise.[1]

We prefer the first alternative. From this point of view, the
decisive event to which Kant is referring is his reading of
Hume's Enquiry (in translation) during the late 1750s to
mid 1760s, and this event, we believe, is clearly reflected in two
important writings of the mid 1760s: the Attempt to Introduce
the Concept of Negative Magnitudes into Philosophy (1763) and
Dreams of a Spirit-Seer Explained by Dreams of Metaphysics
(1766).

In the first (1763) essay Kant introduces the distinction between
“logical grounds” and “real grounds,” both of
which indicate a relationship between a “ground” (cause or
reason) and a “consequent” (following from this
ground). Kant explains his problem as follows (2, 202;
239):

I understand very well how a consequent may be posited through a
ground in accordance with the rule of identity, because it is found to
be contained in [the ground] by the analysis of concepts. …
[A]nd I can clearly comprehend this connection of the ground with the
consequent, because the consequent is actually identical with part of
the concept of the ground …. However, how something may flow
from another, but not in accordance with the rule of identity, is
something that I would very much like to have made clear to me. I call
the first kind of ground a logical ground, because its relation to the
consequent can be logically comprehended in accordance with the rule
of identity, but I call the second kind of ground a real ground,
because this relation indeed belongs to my true concepts, but the
manner of this [relation] can in no way be estimated. With respect to
such a real ground and its relation to the consequent, I pose my
question in this simple form: how can I understand the circumstance
that, because something is, something else is to be? A
logical consequent is only posited because it is identical with the
ground.

The fundamental problem with the relationship between a real ground
and its consequent, therefore, is that the consequent is
not identical with either the ground or a part of this
concept—i.e., it is not “contained in [the
ground] by the analysis of concepts.”

Thus, using his well-known later terminology (from the
Critique and the Prolegomena), Kant is here saying
that, in the case of a real ground, the relationship between the
concept of the consequent (e.g., an effect) and the concept of the
ground (e.g., a cause) is not one of containment, and the judgment
that the former follows from the latter is therefore not
analytic. Moreover, although Kant does not explicitly refer
to Hume in the essay on Negative Magnitudes, he proceeds to
illustrate his problem with an example (among others) of the causal
connection in the communication of motion by impact (2, 202; 240):
“A body A is in motion, another B is at rest
in the straight line [of this motion]. The motion of A is
something, that of B is something else, and, nevertheless,
the latter is posited through the former.” Hume famously uses
this example (among others) in the Enquiry to illustrate his
thesis that cause and effect are entirely distinct events, where the
idea of the latter is in no way contained in the idea of the former
(EHU 4.9; SBN 29): “The mind can never possibly find the effect
in the supposed cause, by the most accurate scrutiny and
examination. For the effect is totally different from the cause, and
consequently can never be discovered in it. Motion in the second
billiard-ball is a quite distinct event from motion in the first; nor
is there anything in the one to suggest the smallest hint of the
other.” A few lines later Hume describes this example as follows
(EHU 4.10; SBN 29): “When I see, for instance, a billiard-ball
moving in a straight line towards another; even suppose motion in the
second ball should by accident be suggested to me, as the result of
their contact or impulse; may I not conceive, that a hundred different
events might as well follow from the cause? … All these
suppositions are consistent and conceivable.”

In Kant's second essay from this period, Dreams of a
Spirit-Seer (1766), he goes further: he suggests a Humean
solution to the problem he had posed, but did not solve, in the essay
on Negative Magnitudes. Kant suggests, more specifically,
that the relation between a real ground and its consequent can only be
given by experience (2, 370; 356):

It is impossible ever to comprehend through reason how something could
be a cause or have a force, rather these relations must be taken
solely from experience. For the rule of our reason extends only to
comparison in accordance with identity and
contradiction. But, in so far as something is a cause, then,
through something, something else is posited, and
there is thus no connection in virtue of agreement to be
found—just as no contradiction will ever arise if I wish to view
the former not as a cause, because there is no contradiction [in the
supposition that] if something is posited, something else is
cancelled. Therefore, if they are not derived from experience, the
fundamental concepts of things as causes, of forces and activities,
are completely arbitrary and can neither be proved nor
refuted.

This passage seems clearly to recall the main ideas in section 4, part
1 of Hume's Enquiry. After distinguishing between
“relations of ideas” and “matters of fact,”
and asserting that the former “are discoverable by the mere
operation of thought” (EHU 4.1; SBN 25), Hume continues (EHU
4.2; SBN 25): “Matters of fact, which are the second objects of
human reason, are not ascertained in the same manner; nor is our
evidence of their truth, however great, of a like nature with the
foregoing. The contrary of every matter of fact is still possible;
because it can never imply a contradiction ….” Hume then
explains that: “all reasonings concerning matters of fact seem
to be founded on the relation of Cause and Effect” (EHU
4.4; SBN 26) and adds (EHU 4.6; SBN 27): “I shall venture to
affirm, as a general proposition, which admits of no exception, that
the knowledge of this relation is not, in any instance, attained by
reasonings a priori; but arises entirely from experience,
when we find that any particular objects are constantly conjoined with
each other.” Finally (EHU 4.10; SBN 29): “And as the first
imagination or invention of a particular effect, in all natural
operations, is arbitrary, where we consult not experience; so must we
also esteem the supposed tye or connexion between the cause and
effect, which binds them together, and renders it impossible that any
other effect could result from the operation of that cause.”
Thus, although Kant does not explicitly mention Hume in Dreams of
a Spirit-Seer, the parallels with Hume's Enquiry are
striking
indeed.[2]

Kant does not endorse a Humean solution to the problem of the
relation between cause and effect in the critical period (beginning
with the first edition of the Critique in 1781): he does
not (as he had in Dreams of a Spirit-Seer) claim that this
relation is derived from experience. Instead (as we have seen)
Kant takes Hume's problem of causality to be centrally implicated
in the radically new problem of synthetic a priori judgments.
Yet the latter problem, in turn, clearly has its origin in Kant's
earlier discussion (in the essay on Negative Magnitudes and
Dreams of a Spirit-Seer) of the apparently mysterious
connection between a real ground (or cause) and its consequent (or
effect). Just as Kant had earlier emphasized (in these
pre-critical works) that the consequent of a real ground is not
contained in it, and thus does not result by “the analysis of
concepts,” Kant now (in the critical period) maintains that the
concept of the effect cannot be contained in the concept of the cause
and, accordingly, that a judgment relating the two cannot be
analytic. Such a judgment, in Kant's critical terminology,
must now be synthetic—it is a judgment in which “the
connection of the predicate with the subject … is thought
without identity,” where “a predicate is added to the
concept of the subject which is by no means thought in it, and which
could not have been extracted from it by any analysis”
(A7/B10–11). The crucial point about a synthetic a
priori judgment, however, is that, although it is certainly not
(as a priori) derived from experience, it nonetheless extends our
knowledge beyond merely analytic judgments.

It therefore becomes clear why, in the Introduction to the second
edition of the Critique, Kant says of the crucial problem of
synthetic a priori judgments that “this problem, and perhaps
even the distinction between analytic and synthetic
judgments, was not thought of earlier,” and then explicitly
names “David Hume, who, among all philosophers, came closest to
this problem” (B19). It also becomes clear why, in
the Preface to the Prolegomena, Kant explains Hume's
problem as follows (4, 257; 7):

Hume proceeded primarily from a single but important
concept of metaphysics, namely, that of the connection of cause
and effect … , and he challenged reason, which here
pretends to have generated this concept in her womb, to give him an
account of by what right she thinks that something could be so
constituted that, if it is posited, something else must necessarily
also be posited thereby; for this is what the concept of cause
says. He proved indisputably that it is completely impossible for
reason to think such a connection a priori and from concepts [alone]
(for this [connection] contains necessity); but it can in no way be
comprehended how, because something is, something else must
necessarily also be, and how, therefore, the concept of such a
connection could be introduced a priori.

Thus here, in the Prolegomena, Kant describes what he calls
Hume's “challenge” to reason concerning “the
connection of cause and effect” in precisely the same terms
that he had himself earlier used, in the 1763 essay on Negative
Magnitudes and the 1766 Dreams of a Spirit-Seer, to pose
a fundamental problem about the relation of a real ground (as opposed
to a logical ground) to its consequent.

What is most important, however, is the official solution to
Hume's problem that Kant presents in § 29 of the
Prolegomena. This solution depends on the distinction
between “judgments of perception” and “judgments of
experience” which Kant has extensively discussed in the preceding
sections. In § 18 Kant introduces the distinction as follows
(4, 298; 51):

Empirical judgments, in so far as they have objective
validity, are judgments of experience; they,
however, in so far as they are only subjectively valid, I
call mere judgments of perception. … All of
our judgments are at first mere judgments of perception: they are
valid merely for us, i.e., for our subject, and only afterwards do we
give them a new relation, namely to an object, and we intend that [the
judgment] is supposed to be also valid for us at all times and
precisely so for everyone else; for, if a judgment agrees with an
object, then all judgments about the same object must also agree
among one another, and thus the objective validity of the judgment of
experience signifies nothing else but its necessary universal
validity.

Then, in § 22, Kant emphasizes that the pure concepts of the
understanding or categories function precisely to convert mere
(subjective) perceptions into objective experience by effecting a
“necessary unification” of them (4, 305; 58):
“Therefore, the pure concepts of the understanding are those
concepts under which all perceptions must first be subsumed before
they can serve as judgments of experience, in which the synthetic
unity of perceptions is represented as necessary and universally
valid.”[3]
Here is how Kant formulates his solution in § 29 (4, 312;
65):

In order to make a trial with Hume's problematic concept (his
crux metaphysicorum), namely the concept of cause,
first, there is given to me a priori, by means of logic, the form of a
conditional judgment in general, namely, to use a given cognition as
ground and the other as consequent. It is possible, however, that a
rule of relation is found in perception which says that a given
appearance is constantly followed by another (but not conversely); and
this is a case for me to employ the hypothetical judgment and, e.g.,
to say: if a body is illuminated sufficiently long by the sun, then it
becomes warm. Here, there is certainly no necessity of connection as
yet, and thus [not] the concept of cause. However, I continue and say
that, if the above proposition, which is merely a subjective
connection of perceptions, is to be a judgment of experience, then
it must be viewed as necessary and universally valid. But such a
proposition would be: the sun is through its light the cause of
heat. The above empirical rule is now viewed as a law—and, in
fact, not as valid merely of appearances, but [valid] of them on
behalf of a possible experience, which requires completely and thus
necessarily valid rules.

All the elements from Kant's earlier discussion of causality
in the essays on Negative Magnitudes and Dreams of a
Spirit-Seer seem to be present here. Kant begins with the
purely logical relation between ground and consequent. Since, in
the case of the concept of cause, we are dealing with what Kant had
earlier called a real ground, Kant holds that we need a
synthetic rather than merely analytic connection between the two.
The most obvious thought, which Hume had defended in the
Enquiry (and, apparently following Hume, Kant himself had
defended in Dreams of a Spirit-Seer) is that
“experience” (in the Humean sense) is the basis for this
connection in so far as one perception is found to be “constantly
conjoined” with another. Now, however, in the critical
period, Kant introduces a revolutionary new concept of
“experience” which is explicitly opposed to mere constant
conjunctions among perceptions in being “necessary and
universally valid”—in particular, “experience is
possible only by means of the representation of a necessary connection
of perceptions” (B218).

In Kant's example from § 29 of the Prolegomena,
then, we begin from a mere subjective “empirical
rule”: that the perception of an illuminated stone is
constantly followed by the perception of heat; and we then convert this
“empirical rule” into an objective law according to which
the very same relationship is now viewed as “necessary and
universally valid.” This transformation is effected
by the addition of the a priori concept of causality: “the
sun is through its light the cause of heat.” It is in
precisely this way, more generally, that the categories or pure
concepts of the understanding relate to experience:
“not in such a way that they are derived from experience, but that
experience is derived from them, a completely reversed kind of
connection which never occurred to Hume” (§ 30: 4, 313;
66).

We shall devote the rest of this article to clarifying Kant's
solution and its relationship with Hume's conception of
causation. For now, we simply note an important difficulty Kant
himself raises in the Prolegomena. Whereas the concept
of causality is, for Kant, clearly a priori, he does not think that
particular causal laws relating specific causes with specific effects
are all synthetic a priori—and, if they are not a priori, how can
they be necessary? Indeed, Kant illustrates this difficulty, in a
footnote to § 22, with his own example of the sun warming a stone
(4, 305; 58):

But how does this proposition, that judgments of experience are
supposed to contain necessity in the synthesis of perceptions, agree
with my proposition, urged many times above, that experience, as a
posteriori cognition, can yield only contingent judgments? If I say
that experience teaches me something, I always mean only the
perception that lies within in it, e.g., that heat always follows the
illumination of the stone by the sun. That this heating results
necessarily from the illumination by the sun is in fact contained in
the judgment of experience (in virtue of the concept of cause); but I
do not learn this from experience, rather, conversely, experience is
first generated through this addition of the concept of the
understanding (of cause) to the perception.

In other words, experience in the Humean sense teaches me that heat
always (i.e., constantly) follows the illumination of the stone by the
sun; experience in the Kantian sense then adds that: “the
succession is necessary; … the effect does not merely
follow upon the cause but is posited through it and
follows from it” (A91/B124). But what exactly does
this mean?

Kant formulates a crucial distinction between
“strict” and “comparative” universality in
§ II of the Introduction to the second edition of the
Critique (B3–4):

Experience never gives its
judgments true or strict, but merely assumed or comparative
universality (through induction), so that, properly speaking,
it must be formulated: so far as we have observed until now, no
exception has been found to this or that rule. If, therefore, a
judgment is thought with strict universality, i.e., so that no
exception at all is allowed to be possible, then it is not derived from
experience, but is valid absolutely a priori. Empirical
universality is thus only an arbitrary augmentation of validity from
that which is valid in most cases to that which is valid in
all—as, e.g., in the proposition: all bodies are
heavy. By contrast, where strict universality essentially belongs
to a judgment, this [universality] indicates a special source of
cognition for [the judgment], namely a faculty of a priori
cognition. Necessity and strict universality are thus secure
criteria of an a priori cognition, and also inseparably belong
together.

Kant then explicitly links this distinction to Hume's discussion of
causality in the following paragraph (B5): “The very concept of
cause so obviously contains the concept of a necessity of the
connection with an effect and a strict universality of the rule, that
the concept [of cause] would be entirely lost if one pretended to
derive it, as Hume did, from a frequent association of that which
happens with that which precedes, and [from] a thereby arising custom
(thus a merely subjective necessity) of
connecting
representations.”[4]
Moreover, in the second edition (as we have seen) Kant also goes on
to name Hume explicitly, as one who attempted to derive the concept of
causality “from a subjective necessity arising from frequent
association in experience—i.e., from custom—which
is subsequently falsely taken for objective” (B127). It
appears, therefore, that Kant's discussion, in § 29 of the
Prolegomena, of how, by the addition of the concept of cause,
we convert a mere subjective “empirical rule” into an
objective law (which is “necessary and universally valid”),
is not only indebted to Hume for the insight that the connection
between cause and effect is synthetic rather than analytic, it is also
indebted to Hume's discussions of the problem of induction (in
section 4, part 2 of the Enquiry) and of the idea of necessary
connection (in section 7). Kant agrees with Hume that the idea of
necessary connection is in fact an essential ingredient in our idea of
the relation between cause and effect; Kant agrees, in
addition, that, if all we had to go on were a purely inductive
inference from observed constant conjunctions, the inference from
comparative to strict universality would not be legitimate, and the
presumed necessary connection arising in this way (i.e., from custom)
would be merely subjective.

Section 4 of the Enquiry is entitled “Sceptical Doubts
Concerning the Operations of the Understanding.” In part 1 of
this section (as we have already seen) Hume maintains that the idea of
the effect is never contained in the idea of the cause (in Kant's
terminology, the relation is not analytic), and thus, according to
Hume, it is never knowable a priori. We therefore need experience in
the Humean sense in order to make any causal claims—that is, the
observation of an event of one type A constantly followed by an event
of another type B. Otherwise (as we have also seen) any event could
follow any other (EHU 4.10; SBN 29): “And as the first
imagination or invention of a particular effect, in all natural
operations, is arbitrary, where we consult not experience; so must we
also esteem the supposed tye or connexion between the cause and
effect, which binds them together, and renders it impossible that any
other effect could result from the operation of that cause.”
Note that Hume is here supposing that, in our idea of the relation
between cause and effect, the “tye or connexion … which
binds them together” is necessary (“it is impossible that
any other effect could result”). In the corresponding section of
the Treatise, Book 1, part 3, section 2 (“Of
probability; and of the idea of cause and effect”), Hume makes
this completely explicit (T 1.3.2.11; SBN 77): “Shall we then
rest contented with these two relations of contiguity and succession,
as affording a compleat idea of causation? By no means. An object may
be continuous and prior to another, without being consider'd as its
cause. There is a NECESSARY CONNEXION to be taken into consideration;
and that relation is of much greater importance, than any of the other
two above-mention'd.”

In the Enquiry, section 4, part 2, Hume presents his famous
skeptical argument concerning causation and induction. Since we need
“experience” (i.e., the observation of constant
conjunctions) to make any causal claims, Hume now asks (EHU 4.14; SBN
32): “What is the foundation of all conclusions from
experience?” The conclusion from an experience of constant
conjunction is an inference to what has not yet been observed from
what has already been observed, and Hume finds an unbridgeable gap
between the premise (summarizing what we have observed so far) and the
(not yet observed) conclusion of this inference (EHU 4.16; SBN 34):
“These two propositions are far from being the same, I have
found that such an object has always been attended with such an
effect, and I foresee, that other objects, which are, in
appearance, similar, will be attended with similar effects.”
Hume concludes that this inference has no foundation in the
understanding—that is, no foundation in what he calls
“reasoning.”[5]
How does Hume arrive at this position?

All our inductive inferences—our “conclusions from
experience”—are founded on the supposition that the course
of nature is sufficiently uniform so that the future will be
conformable to the past (EHU 4.21; SBN 37–38): “For all
inferences from experience suppose, as their foundation, that the
future will resemble the past …. If there be any suspicion,
that the course of nature may change, and that the past may be no rule
for the future, all experience becomes useless, and can give rise to
no inference or conclusion.” Therefore, what Hume is now
seeking, in turn, is the foundation in our reasoning for the
supposition that nature is sufficiently uniform.

Section 4, part 1 of the Enquiry distinguishes (as we have
seen) between reasoning concerning relations of ideas and reasoning
concerning matters of fact and existence. Demonstrative reasoning
(concerning relations of ideas) cannot establish the supposition in
question, “since it implies no contradiction, that the course of
nature may change, and that an object, seemingly like those which we
have experienced, may be attended with different or contrary
effects” (EHU 4.18; SBN 35). Moreover, reasoning concerning
matters of fact and existence cannot establish it either, since such
reasoning is always founded on the relation of cause and effect, the
very relation we are now attempting to found in reasoning (EHU 4.19;
SBN 35–36): “We have said, that all arguments concerning
existence are founded on the relation of cause and effect; that our
knowledge of that relation is derived entirely from experience; and
that all our experimental conclusions proceed upon the supposition,
that the future will be conformable to the past. To endeavour,
therefore, the proof of this last proposition by probable arguments,
or arguments regarding existence, must be evidently going in a circle,
and taking that for granted, which is the very point in
question.”[6]

Although Hume has now shown that there is no foundation for the
supposition that nature is sufficiently uniform in reasoning or the
understanding, he goes on, in the following section 5 of the
Enquiry (“Skeptical Solution of these Doubts”), to
insist that we are nonetheless always determined to proceed in
accordance with this supposition. There is a natural basis or
“principle” for all our arguments from experience, even if
there is no ultimate foundation in reasoning (EHU 5.4–5; SBN
42–43):

And though [one] should be convinced, that his understanding has no
part in the operation, he would nonetheless continue in the same
course of thinking. There is some other principle, which determines
him to form such a conclusion. This principle is CUSTOM or HABIT. For
wherever the repetition of any particular act or operation produces a
propensity to renew the same act or operation, without being impelled
by any reasoning or process of the understanding; we always say, that
this propensity is the effect of Custom. By employing that
word, we pretend not to have given the ultimate reason of such a
propensity. We only point out a principle of human nature, which is
universally acknowledged, and which is well known by its
effects.[7]

In section 7 of the Enquiry (“On the Idea of
Necessary Connexion”), after rejecting the received views of
causal necessity, Hume explains that precisely this custom or habit
also produces our idea of necessary connection (EHU 7.28; SBN
75):

It appears, then, that this idea of a necessary connexion among events
arises from a number of similar instances which occur of the constant
conjunction of these events; nor can that idea ever be suggested by
any one of these instances, surveyed in all possible lights and
positions. But there is nothing in a number of instances, different
from every single instance, which is supposed to be exactly similar;
except only, that after a repetition of similar instances, the mind is
carried by habit, upon the appearance of one event, to expect its
usual attendant, and to believe that it will exist. This connexion,
therefore, which we feel in the mind, this customary
transition of the imagination from one object to its usual attendant,
is the sentiment or impression, from which we form the idea of power
or necessary connexion.

Thus, the custom or habit to make the inductive inference not only
gives rise to a new idea of not yet observed instances resembling the
instances we have already observed, it also produces a feeling of
determination to make the very inductive inference in question.
This feeling of determination, in turn, gives rise to a further new
idea, the idea of necessary connexion, which has no resemblance
whatsoever with anything we have observed. It is derived from an
“impression of reflection” (an internal feeling or
sentiment), not from an “impression of sensation” (an
observed instance before the mind), and it is in precisely this sense,
for Hume, that the idea of necessary connection is merely
subjective. Hume emphasizes that this is a
“discovery” both “new and extraordinary,” and
that it is skeptical in character (EHU 7.28–29; SBN 76):
“No conclusions can be more agreeable to scepticism than such as
make discoveries concerning the weakness and narrow limits of human
reason and capacity. And what stronger instance can be produced
of the surprising ignorance and weakness of the understanding, than the
present? For surely, if there be any relation among objects,
which it imports to us to know perfectly, it is that of cause and
effect.”

Kant agrees with Hume that neither the relation of cause and effect
nor the idea of necessary connection is given in our sensory
perceptions; both, in an important sense, are contributed by our
mind. For Kant, however, the concepts of both causality and
necessity arise from precisely the operations of our
understanding—and, indeed, they arise entirely a priori as pure
concepts or categories of the understanding. It is in precisely
this way that Kant thinks that he has an answer to Hume's
skeptical problem of induction: the problem, in Kant's
terms, of grounding the transition from merely
“comparative” to “strict universality”
(A91–92/B123–124). Thus in § 29 of the
Prolegomena, as we have seen, Kant begins from a merely
subjective “empirical rule” of constant conjunction or
association among our perceptions (of heat following illumination by
the sun), which is then transformed into a “necessary and
universally valid law” by adding the a priori concept of
cause.

At the end of our discussion in section 1 above we saw that there is a
serious difficulty in understanding what Kant intends here—a
difficulty to which he himself explicitly calls attention. Kant does
not think that the particular causal law that “the sun is
through its light the cause of heat” is itself a synthetic a
priori truth. Indeed, the very same difficulty is present in our
discussion at the beginning of this section. For, what Kant is saying
in § II of the second edition of the Introduction to the
Critique is that necessity and strict universality are
“secure criteria of an a priori cognition” (B4;
emphasis added). More specifically (B3): “Experience in fact
teaches us that something is constituted thus and so, but not that it
cannot be otherwise. Hence, if … a proposition is thought
together with its necessity, then it is an a priori
judgment.” Yet, once again, Kant does not think that particular
causal laws relating specific causes to specific effects are all
(synthetic) a priori. Accordingly, when Kant provides examples of
(synthetic) a priori cognitions in the immediately following
paragraph, he cites the synthetic a priori principle of the Second
Analogy of Experience (“All alterations take place in accordance
with the law of the connection of cause and effect” [B232])
rather than any particular causal law (B4–5): “Now it is
easy to show that there actually are such judgments in human
cognition which are necessary and in the strictest sense universal,
and therefore purely a priori. If one wants an example from the
sciences, then one need only take a look at any of the propositions of
mathematics. If one wants such an example from the most common use of
the understanding, then the proposition that every alteration must
have a cause can serve.”

On the basis of this important passage, among others, the majority
of twentieth-century English-language commentators have rejected the
idea that Kant has a genuine disagreement with Hume over the status of
particular causal laws. One must sharply distinguish between the
general principle of causality of the Second Analogy—the
principle that every event b must have a cause a—and particular
causal laws: particular instantiations of the claim that all
events of type A must always be followed by events of type B. The
former is in fact a synthetic a priori necessary truth holding as a
transcendental principle of nature in general, and this principle is
explicitly established in the Second Analogy. But the Second
Analogy does not establish, on this view, that particular causal laws
are themselves necessary. Indeed, as far as particular causal
laws are concerned, the Second Analogy is in basic agreement with
Hume: they (as synthetic a posteriori) are established
by induction and by induction
alone.[8]

It is indeed crucially important to distinguish between the general
principle of causality Kant establishes in the Second Analogy and
particular causal laws. It is equally important that particular causal
laws, for Kant, are (at least for the most part) synthetic a
posteriori rather than synthetic a priori. It does not follow,
however, that Kant agrees with Hume about the status of synthetic a
posteriori causal laws. On the contrary, Kant (as we have seen)
clearly states, in § 29 of the Prolegomena (the very
passage where he gives his official “answer to Hume”),
that there is a fundamental difference between a mere “empirical
rule” (heat always follows illumination by the sun) and a
genuine objective law (the sun is through its light the cause of heat)
arrived at by adding the a priori concept of cause to the merely
inductive rule. Any law thus obtained is “necessary and
universally valid,” or, as Kant also puts it, we are now in
possession of “completely and thus necessarily valid
rules.” In such cases (A91/B124): “The succession is
necessary; … the effect does not merely follow upon
the cause but is posited through it and follows from
it. The strict universality of the rule is certainly not a property of
empirical rules, which, through induction, can acquire nothing but
comparative universality: i.e., extensive utility.” Therefore,
it is by no means the case that Kant simply agrees with Hume that
particular causal laws are grounded solely on induction and,
accordingly, that the necessity we attribute to particular causal
connections is merely subjective.

Similarly, the text of the Second Analogy is also committed to the
necessity and strict universality of particular causal laws. If
the general causal principle (that every event b must have a cause a)
is true, then, according to Kant, there must also be particular causal
laws (relating preceding events of type A to succeeding events of type
B) which are themselves strictly universal and
necessary.[9]
Kant maintains that, when
one event follows another in virtue of a causal relation, it must
always follow “in accordance with a rule”
(A193/B238). Moreover, the “rule” to which Kant is
here referring is not the general causal principle, but rather a
particular law connecting a given cause to a given effect which is
itself strictly universal and necessary (A193/B238–239):
“In accordance with such a rule, there must thus lie in that
which precedes an event as such the condition for a rule according to
which this event follows always and necessarily.” Kant
insists on this point throughout the Second Analogy: “that
which follows or happens must follow according to a universal rule from
that which was contained in the previous state” (A200/B245),
“in that which precedes the condition is to be met with under
which the event always (i.e., necessarily) follows” (A200/B246),
and so on. One cannot escape the burden of explaining the
apparently paradoxical necessity and universal validity of particular
(synthetic) a posteriori causal laws simply by distinguishing
them from the general (synthetic) a priori causal
principle.

What is the relationship, then, between the general causal principle
of the Second Analogy and the particular causal laws whose existence,
according to Kant, is required by the causal principle? What,
more generally, is the relationship between the transcendental
synthetic a priori principles of the understanding (including all three
Analogies of Experience—compare the end of note 3 above—as
well as the principles corresponding to the other categories) and the
more particular synthetic a posteriori laws of nature involved in
specific causal relationships governing empirically characterized
events and processes? The relationship cannot be deductive; for,
if one could deductively derive the particular causal laws from the
transcendental principles of the understanding, then the former would
have to be synthetic a priori as well.

Kant himself discusses this relationship extensively, beginning in
the first edition version of the Transcendental Deduction
(A126–128):

Although we learn many laws through experience, these are still only
particular determinations of yet higher laws, among which the highest
(under which all others stand) originate a priori in the understanding
itself, and are not borrowed from experience, but must rather provide
appearances with their law-governedness, and precisely thereby make
experience possible … To be sure, empirical laws as such can in
no way derive their origin from pure understanding—no more than
the immeasurable manifold of appearances can be sufficiently
comprehended from the pure form of sensibility. But all empirical laws
are only particular determinations of the pure laws of the
understanding, under which and in accordance with the norm of which
they first become possible, and the appearances take on a lawful
form—just as all appearances, notwithstanding the diversity of
their empirical form, still must also always be in accordance with the
condition of the pure form of sensibility [i.e., space and
time].

The “pure laws of the understanding” (here and elsewhere)
refers to the pure transcendental principles of the
understanding characterizing what Kant calls “experience in
general” or “nature in general.”

In the second edition version Kant makes essentially the same point,
this time explicitly stating that the relationship in question is not
deductive (B165):

The pure faculty of understanding, however, is not sufficient for
prescribing to appearances a priori, through mere categories, any laws
other than those which are involved in a nature in general,
as the law-governedness of all appearances in space and
time. Particular laws, because they concern empirically determined
appearances, can not be completely derived therefrom,
although they one and all stand under them. Experience must be added
in order to become acquainted with the [particular laws] as
such, but only the former laws provide a priori instruction
concerning experience in general, and [concerning] that which can be
cognized as an object of experience.

But what exactly does it mean for particular laws of nature to
“stand under” the a priori principles of the
understanding—that is, to be what Kant calls “particular
determinations” of these principles? Once again, it will
take more work fully to clarify this relationship, but we can meanwhile
observe that it is precisely in virtue of the relationship in question
that empirical causal connections—empirical causal laws of
nature—count as necessary for Kant.

The necessity in question is characterized in Kant's official
discussion of the category of necessity in the Postulates of
Empirical Thought—the three principles corresponding to the
categories of possibility, actuality, and necessity
(A218–218/B265–266):

That which agrees with the formal conditions of experience
(according to intuition and concepts), is possible.

That which coheres with the material conditions of experience
(with sensation), is actual.

That whose coherence with the actual is determined in accordance
with the general conditions of experience, is (exists as)
necessary.

The “formal [or “general”] conditions of
experience” include the forms of intuition (space and time),
together with all the categories and principles of the
understanding. The material conditions of experience include that
which is given to us, through sensation, in perception. Kant is thus
describing a three-stage procedure, in which we begin with the formal
a priori conditions of the possibility of experience in
general, perceive various actual events and processes by
means of sensation, and then assemble these events and processes
together—via necessary connections—by means of
the general conditions of the possibility of experience with which we
began.

In his detailed discussion of the third Postulate Kant makes it clear
that he is referring, more specifically, to causal
necessity, and to particular (empirical) causal laws
(A226–8/B279–80): “Finally, as far as the
third Postulate is concerned, it pertains to material
necessity in existence, and not the merely formal and logical
necessity in the connection of concepts. … Now there is no
existence that could be cognized as necessary under the condition of
other given appearances except the existence of effects from given
causes in accordance with laws of causality. Thus, it is not the
existence of things (substances), but only that of their state, about
which we can cognize their necessity—and, indeed, from other
states that are given in perception, in accordance with empirical laws
of causality.” Note that, in this passage, Kant refers to
“laws of causality” (in the plural) in the second quoted
sentence, and “empirical laws of causality” (again in the
plural) in the last sentence. Hence, he is here referring to
particular causal laws (of the form every event of type A
must always be followed by an event of type B) rather than
the general principle of the Second Analogy (that every event
b must have a cause
a).[10]

In the Transcendental Deduction (as we have seen) Kant says that
“all empirical laws are only particular determinations of the
pure laws of the understanding, under which and in accordance with the
norm of which they first become possible, and the appearances take on a
lawful form” (A127–128). In the discussion of the third
Postulate Kant says that we can cognize an effect as necessary
on the basis of an empirical law relating it to its cause—where
the effect's “connection with the actual is determined in
accordance with the general conditions of experience”
(A218/B266). Kant is suggesting, therefore, that the precise
sense in which particular empirical laws themselves become necessary is
that they, too, are “determined” in relation to actual
perceptions “in accordance with the general conditions of
experience” (where the latter, of course, essentially
include the “pure laws of the understanding,” i.e., the
principles).

Thus, in the example from § 29 of the Prolegomena,
Kant begins from a mere “empirical rule” (that heat always
follows illumination by the sun) and then proceeds to a
“necessary and universally valid” law by adding the a
priori concept of cause to this (so far) merely inductive rule.
The very same three-stage procedure described by the three Postulates
as a whole—in which we begin with the formal a priori conditions
of the possibility of experience in general, perceive various
actual events and processes by means of sensation, and then
assemble these events and processes together (via necessary
connections) by means of the a priori conditions of the possibility of
experience—also results in “necessary and universally
valid” empirical causal laws of nature (the sun is through its
light the cause of heat) governing the events and processes in
question.

In § 36 of the Prolegomena (after he has presented his
official “answer to Hume” in § 29) Kant addresses the
question of the relationship between particular empirical laws and the
a priori principles of the understanding under the title “How is
nature itself possible?” Nature in the material
sense is “the totality of all appearances” given in space
and time (4, 318; 69). Nature in the formal sense is
“the totality of rules under which all appearances must stand if
they are to be thought as connected in an experience” (4, 318;
70). In answering the question of how nature in the formal sense
is possible Kant proceeds to distinguish between “empirical laws
of nature, which always presuppose particular perceptions” and
“the pure or universal laws of nature, which, without having a
basis in particular perceptions, contain merely the conditions of their
necessary unification in an experience” (4, 320; 71).

Yet (as we have seen) the empirical laws owe their status as
“necessary and universally valid” to their relationship
with the a priori “pure or universal” laws
(principles) of the understanding. Moreover, Kant illustrates
this situation with an example, which (as explained in the very brief
§ 37) “is to show, that laws that we discover in objects of
sensible intuition, especially if they are cognized as necessary, are
already taken by us to be such as the understanding has put there, even
though they are otherwise similar in all respects to laws of nature
that we attribute to experience” (4, 320; 72). The example
(presented in the immediately following § 38) is a “physical
law of mutual attraction, extending over the whole of material nature,
whose rule is that it diminishes inversely with the square of the
distances from every attracting point” (4, 321; 73). Thus,
Kant illustrates his conception of the relationship between particular
empirical laws and the a priori principles of the understanding with
the Newtonian law of universal
gravitation.[11]

In § VI of the Introduction to the second edition of the
Critique, where Kant discusses the “general problem of
pure reason” (“How are synthetic a priori judgments
possible?”), Kant explains that “in the solution of [this]
problem there is also conceived, at the same time, the possibility of
the pure employment of reason in grounding and developing all sciences
that contain a theoretical a priori cognition of objects, i.e., the
answer to the questions: How is pure mathematics possible? How
is pure natural science possible?” (B20). Kant
illustrates his contention that propositions of “pure natural
science” actually exist in a footnote (ibid.): “One need
only attend to the various propositions that appear at the beginning
of proper (empirical) physics, such as those of the permanence of the
same quantity of matter, of inertia, of the equality of action and
reaction, and so on, in order to be soon convinced that they
constitute a pure (or rational) physics, which well deserves, as a
science of its own, to be isolated and established in its entire
extent, be it narrow or wide.”

Kant had just completed the latter task, in fact, in his
Metaphysical Foundations of Natural Science, which had
meanwhile appeared in 1786 (following the publication of the
Prolegomena in 1783 and immediately preceding the publication
of the second edition of the Critique in 1787). There
Kant articulates what he calls “pure natural science” in
four chapters corresponding, respectively, to the four headings of the
table of categories (quantity, quality, relation, and modality).
In the third chapter or Mechanics (corresponding to the three categories
of relation: substance, causality, and community) Kant derives
three “laws of mechanics” corresponding, respectively, to
the three Analogies of Experience: the permanence or conservation
of the total quantity of matter, the law of inertia, and the equality
of action and reaction—which Kant describes as a law of
“the communication of motion” (4, 544; 84). All these
laws, Kant makes clear, are synthetic a priori propositions,
demonstrated a priori and “drawn from the essence of the thinking
faculty itself” (4, 472; 8).

For Kant, therefore, the laws of the Newtonian science of nature are
of two essentially different kinds. Kant regards Newton's
three “Axioms or Laws of Motion” presented at the beginning
of the Principia as synthetic a priori truths—which Kant
himself attempts to demonstrate a priori in the Metaphysical
Foundations.[12]
By
contrast, Kant does not regard the inverse-square law of universal
gravitation, which Newton establishes by a famous “deduction from
the phenomena” in Book 3 of the Principia, as a
synthetic a priori truth—and, accordingly, Kant does not attempt
to demonstrate this law a priori in the Metaphysical
Foundations. Nevertheless, Kant regards the synthetic a
posteriori law of universal gravitation as “necessary and
universally valid” in virtue of the way in which it is
“determined” in relation to the “phenomena” by
the synthetic a priori laws of pure natural science. And, since
the latter, in turn, are “determined” from the a priori
principles of the understanding, the a posteriori law of universal
gravitation is thereby “determined” in relation to actual
perceptions “in accordance with the general conditions
of
experience.”[13]

We shall return to Kant's conception of Newtonian natural
science below, but we first want to discuss Hume's rather
different debt to Newton. Hume, like virtually everyone else in
the eighteenth century (including Kant), takes Newtonian natural
science as his model, and, indeed, he attempts to develop his own
“science of human nature” following Newton's
example. Yet Hume learns a very different lesson from Newton than
does Kant, based on Newtonian inductivism rather than Newtonian
mathematical demonstrations. Contrasting Hume and Kant on this
point greatly illuminates their diverging conceptions of causation and
necessity.

To begin with, Hume does not consider Newton's “Axioms
or Laws of Motion” as a priori in any sense (in Kant's
terminology, neither analytic nor synthetic a priori). All of
these laws, according to Hume, are simply “facts”
inductively derived from (constant and regular) experience. Hume
considers Newton's second law of motion (F = ma) in the
Enquiry, section 4, part 1 (EHU 4.13; SBN 31):
“Thus, it is a law of motion, discovered by experience, that the
moment or force of any body in motion is in the compound ratio or
proportion of its solid contents and its velocity …
. Geometry assists us in the application of this law … ;
but still the discovery of the law itself is owing merely to
experience, and all the abstract reasonings in the world could never
lead us one step towards the knowledge of it.”

One of Newton's main examples of the third law of motion is
the communication of motion by impact or
impulse.[14]
Hume considers such communication of motion in the same section of the
Enquiry (EHU 4.8; SBN 28–29): “We are apt to
imagine, that we could discover these effects by the mere operation of
our reason, without experience. We fancy, that were we brought, on a
sudden, into this world, we would at first have inferred, that one
billiard ball would communicate motion to another upon impulse; and
that we needed not to have waited for the event, in order to pronounce
with certainty concerning it. Such is the influence of custom, that,
where it is strongest, it not only covers our natural ignorance, but
even conceals itself, and seems not to take place, merely because it
is found in the highest degree.”

Finally, in a footnote at the end of part 1 of section 7 (the section
in the Enquiry devoted to the idea of necessary connection),
Hume considers the law of inertia (EHU 7.25n16; SBN 73n1): “I
need not examine at length the vis inertiae which is so much
talked of in the new philosophy, and which is ascribed to matter. We
find by experience, that a body at rest or in motion continues for
ever in its present state, till put from it by some new cause; and
that a body impelled takes as much motion from the impelling body as
it acquires itself. These are facts. When we call this a vis
inertiae, we only mark these facts, without pretending to have
any idea of the inert power.” (Hume here puts the law of inertia and the communication of motion by
impulse together, because both are consequences of a body's
“inherent force [vis insita]” or “inert
force [vis inertiae”] according to Newton's third
definition preceding the Laws of
Motion.[15])
It is clear, therefore, that Hume
views all of Newton's laws of motion as inductively derived
empirical propositions, which (deceptively) appear to be derived from
reason simply because the constant and regular experience on which they
are in fact based is so pervasive.

We believe that Hume's discussion of the communication of
motion by contact or impulse shows his debt to Newton especially
clearly. In section 7, part 1 of the Enquiry Hume is
criticizing the inherited ideas of necessary connection. We
believe that both here and in section 4, part 1, where he rejects any a
priori demonstration of causality, Hume is centrally concerned with the
conception of necessary connection articulated by the mechanical
natural philosophy. This philosophy had taken the communication
of motion by contact or impulse as the paradigm of an a priori
rationally intelligible causal connection, to which all other instances
of causal connection must be reduced. The reduction would take
place by reducing all observable causal relationships to the motions
and impacts of the tiny microscopic parts of
bodies.[16]

In the view of contemporary mechanical philosophers, especially
Huygens and Leibniz, Newton's conception of universal gravitation
involved an entirely unintelligible action at a distance across empty
space. Gravitation could only be acceptable, on their view, if it
were explained, in turn, by vortices of intervening invisible matter
whose tiny microscopic particles effected the apparent attraction of
bodies via impulse. Although both Leibniz and Huygens accepted
Newton's demonstration that the orbits of the satellites of the
major astronomical bodies in the solar system obey the inverse-square
law (the planets with respect to the sun, the moons of Jupiter and
Saturn with respect to their planets, the earth's moon with
respect to the earth), they rejected Newton's unrestricted
generalization of this law to hold between all bodies (and all parts of
bodies) whatsoever. For them, the inverse-square law could be
accepted in astronomy only by taking the major bodies of the solar
system as each being surrounded by vortices limited to the finite
surrounding region of their satellites. The validity of the
inverse-square law would thus be restricted to precisely such a finite
region, so that it could not be extended arbitrarily far: the
moons of Jupiter would accelerate towards Jupiter, for example, but
neither Saturn nor the sun, for example, would experience such
accelerations towards
Jupiter.[17]

In the second (1713) edition of the Principia, in response to these
doubts about the law of universal gravitation raised by mechanical
philosophers, Newton adds an explicit principle of unrestricted
inductive generalization—Rule 3—to a set of “Rules
for the Study of Natural Philosophy” at the beginning of Book
3. Rule 3 states (Principia, 795): “Those qualities of
bodies that cannot be intended and remitted [i.e. qualities that
cannot be increased and diminished] and that belong to all bodies on
which experiments can be made should be taken as qualities of all
bodies
universally.”[18]
Then, in the explanation of this Rule, Newton depicts the hypotheses
of the mechanical philosophy as in conflict with the method of
inductive generalization that leads to the law of universal
gravitation (Principia, 795–796): “For the
qualities of bodies can be known only through experiments; and
therefore qualities that square with experiments universally are to be
regarded as universal qualities …. Certainly idle fancies
ought not to be fabricated recklessly against the evidence of
experiments, nor should we depart from the analogy of nature, since
nature is always simple and ever consonant with itself.”

That the “idle fancies” in question include the hypotheses
of the mechanical philosophers (such as the vortex hypothesis) is made
perfectly clear and explicit in the passage from the General Scholium
(also added to the second edition in 1713) where Newton famously says
that he “feigns” no hypotheses (Principia, 943):
“I have not as yet been able to deduce from phenomena the reason
for [the] properties of gravity, and I do not feign hypotheses. For
whatever is not deduced from the phenomena must be called a
hypothesis; and hypotheses, whether metaphysical or physical, or based
on occult qualities, or mechanical, have no place in experimental
philosophy. In this experimental philosophy, propositions are deduced
from the phenomena and are made general by induction. The
impenetrability, mobility, and impetus of bodies, and the laws of
motion and the law of gravitation have been found by this
method.”[19]
Thus, Newton also makes it clear that gravity is (at least) as well
grounded by induction as the favored properties of bodies singled out
by the mechanical philosophers (impenetrability, motion, and impetus),
all of which have been derived inductively from phenomena (a
point he had earlier developed in the explanation of Rule
3).[20]

Hume (as we have seen) considers all the laws of
motion—including the communication of motion by contact or
impulse—as (merely) inductively derived general principles.
Accordingly, Hume also unreservedly accepts universal gravitation and
takes Newton's theory to articulate a fundamental law of nature
completely on a par with all other inductively established laws (EHU
6.4; SBN 57): “There are some causes, which are entirely uniform
and constant in producing a particular effect; and no instance has
ever yet been found of any failure or irregularity in their
operation. Fire has always burned, and water suffocated every human
creature: The production of motion by impulse and gravity is an
universal law, which has hitherto admitted of no exception.” For
Hume, contrary to the mechanical philosophy, there is absolutely no
asymmetry between the law of universal gravitation and the laws of
impact with respect to their intrinsic
intelligibility.[21]

There is an even more fundamental relationship between Hume's
conception of the inductive method and Newton's Rule 3. In
the explanation of this Rule (as we have seen) Newton takes the
supposition that “nature is always simple and ever consonant with
itself” to license the inductive generalizations made in
accordance with the Rule. Similarly, Hume appeals, in the
Enquiry, to the supposition that “the course of
nature” does not change (EHU 4.21; SBN 37–38) or, equivalently,
that “the future will be conformable to the past” (EHU
4.19; SBN 35–36). In the Treatise Hume formulates this
supposition as the “principle, that instances, of which we
have had no experience, must resemble those, of which we have had
experience, and that the course of nature continues always uniformly
the same” (T 1.3.6.4; SBN 89). Hume takes this
supposition to license (in his own words, to provide the
“foundation” for: compare note 5 above) all inductive
inferences from observed constant conjunctions, just as Newton takes
the supposition that “nature is always simple and ever consonant
with itself” to license the applications of his Rule 3. It
appears very likely, therefore, that Hume takes this Newtonian
supposition as the model for his own principle of the uniformity
of
nature.[22]

Yet Hume raises radical skeptical doubts about this very
principle. It has no foundation in reasoning: neither in
demonstrative reasoning nor (on pain of circularity) in inductive
reasoning itself. Nevertheless, as firmly based in custom or
habit, it is a universal principle of the human mind. Moreover,
it is also the foundation for the best available science of matters of
fact—Newtonian inductive science—and for Hume's own
inductive science (self-consciously following Newton) of
human
nature.[23]
Thus, when Hume sets his
radical skeptical doubts aside, the application of our foremost
empirical scientific method (based on uniform constant conjunction) has
normative force, and it thereby leads to the articulation of universal,
exceptionless laws of nature which, as such, we are compelled to treat
as necessary until experience teaches us otherwise (in accordance with
Newton's Rule 4 in Book 3 of the Principia: see
note 19
above).[24]
It is
because the idea of necessary connection, for Hume, arises from the
application of the Newtonian inductive method that our projection of an
inner feeling of determination onto nature does not merely reduce to a
blind instinctual disposition, but amounts to a normative
methodological standard in our best scientific understanding
of
nature.[25]

In the famous hypothesis non fingo passage from the General
Scholium Newton characterizes his “experimental” method as
follows (Principia, 943): “In this experimental
philosophy, propositions are deduced from the phenomena and are made
general by induction.” Hume focusses exclusively on the second,
inductive, clause, and he thereby shows an especially deep insight
into the fundamental difference between Newton's methodology and the
purely deductive ideal of scientific knowledge represented by the
mechanical philosophy. For Kant, by contrast, the dispute between
Newton and the mechanical philosophers is now effectively over; and
Kant concentrates instead on Newtonian mathematical demonstrations and
the idea of “deduction from phenomena.” This comes out
especially clearly in the
Metaphysical Foundations of Natural Science, where Kant
engages with some of the most important details of Newton's
demonstration of the law of universal gravitation from the initial
“phenomena” described at the beginning of Book 3 of the
Principia. Kant shows especially deep insight into the
way in which this argument is inextricably entangled, in turn, with the
Newtonian mathematical conception of (absolute) space, time, and
motion; and he thereby takes special pains to frame the explicitly
inductive steps in Newton's argument within the a priori
“special metaphysics” of nature expounded in the
Metaphysical Foundations.[26]

The “phenomena” with which Book 3 of the
Principia begins record the observed relative motions of the
principal satellites in the solar system with respect to their primary
bodies (the planets with respect to the sun, the moons of Jupiter and
Saturn with respect to their planets, the earth's moon with
respect to the earth). All of these satellites obey
Kepler's laws (at the time often called “rules”) of
orbital motion; and, appealing to his first law of motion (the law of
inertia), Newton is able to derive purely mathematically that each of
the satellites in question experiences an inverse-square acceleration
directed towards it respective primary body. Moreover, the
so-called “moon test” (developed in Proposition 4 of
Book 3) shows that the inverse-square acceleration governing the
moon's orbit is, when the distance in question approaches the
surface of the earth, numerically equal to the constant acceleration of
terrestrial gravity figuring in Galileo's law of fall.
Newton concludes (by the first and second of his Rules for the Study of
Natural Philosophy) that the (centripetal) force holding the moon in
its orbit is the same force as terrestrial gravity.

The crucial inductive steps come next. Newton generalizes the
result of the moon test to all the other satellites in the solar
system: they, too, are held in their orbits by the same force of
gravity (Proposition 5). Then (in Proposition 6) Newton concludes
that all bodies whatsoever gravitate towards every primary body
(including both Saturn and the sun towards Jupiter, for example);
moreover, their weights, like those of terrestrial bodies, are
proportional to their masses at equal distances from the primary body
in
question.[27]
Finally (in Proposition 7), Newton
applies the third law of motion to this last result to derive the law
of universal gravitation itself: not only do all bodies
whatsoever experience inverse-square accelerations (proportional to
mass) towards every primary body in the solar system, but the primary
bodies themselves experience inverse-square accelerations (proportional
to mass) towards every other body (Jupiter towards its moons and all
other planets, the earth towards its moon and all other planets, and
so
on).[28]
Indeed, Newton here
extends this universal conclusion to the parts of all bodies
as
well.[29]

Kant accepts Newton's law of gravitation in its full universal
form—as a “physical law of mutual attraction, extending
over the whole of material nature, whose rule is that it diminishes
inversely with the square of the distances from every attracting
point” (Prolegomena, § 38: 4, 321; 73).
Moreover, Kant has no qualms at all about action at a distance, and he
even attempts to demonstrate a priori (in the Metaphysical
Foundations) that universal gravitation, as a manifestation of
what he calls the “original” or “fundamental”
force of attraction, must be conceived as an immediate action
at a distance through empty
space.[30]
Kant also attempts to demonstrate
his three “laws of mechanics” corresponding to
Newton's three laws of motion as synthetic a priori truths,
especially the crucially important third law (the equality of action
and
reaction).[31]
Whereas
Newton had devoted considerable effort to producing experimental
evidence for this law (see note 14
above), Kant here ventures a rare criticism
of Newton for not having the courage to prove it a
priori.[32]
Indeed, regarding this
particular law as a synthetic a priori truth is central to Kant's
reinterpretation of the Newtonian concepts of (absolute) space, time,
and motion; for it is in virtue of his understanding of the equality of
action and reaction that Kant is now able simply to define the
center of gravity of the solar system (in which this principle
necessarily holds) as an empirically determinable (provisional)
surrogate for Newtonian absolute
space.[33]
Moreover, and for closely related
reasons, Kant takes the universality of what he calls the
“original” or “fundamental” force of
attraction—that it proceeds from every part of matter to every
other part to infinity—as another synthetic a priori truth
demonstrable in “pure natural
science.”[34]

Given this foundation in “pure natural science,” Kant
then reconstructs Newton's “deduction from the
phenomena” of the law of universal gravitation as follows.
We begin, following Newton, from the observable “phenomena”
described by Kepler's “rules.” These
“phenomena,” in Kant's terminology, are so far mere
“appearances [Erscheinungen],” which have not yet
attained the status of “experience
[Erfahrung].”[35]
Then, again simply
following Newton, we can use the law of inertia to derive (purely
mathematically) inverse-square accelerations of their satellites
directed towards every primary body in the solar system. Once we
have done this, however, we can now, from Kant's point of view,
frame all of Newton's explicitly inductive steps within the a
priori “special metaphysics” of nature developed in the
Metaphysical Foundations. By demonstrating a priori his
three “laws of mechanics” corresponding to the three
Analogies of Experience, Kant establishes that Newton's three
“Axioms or Laws of Motion” are synthetic a priori truths
(compare notes 12 and 31 above). Further, by identifying the
accelerations in question as effects of what Kant calls the fundamental
force of attraction, it now follows from Kant's “special
metaphysics” of (material) nature that these accelerations must
hold immediately between each part of matter and every other part of
matter—and, accordingly, are also directly proportional to
the
mass.[36]

In the fourth chapter or Phenomenology of the Metaphysical
Foundations Kant connects this reconstruction of Newton's
argument with the modal categories of possibility, actuality, and
necessity—the very categories which (as we saw at the end of the
second section above) make it possible for initially merely inductive
generalizations (à la Hume) to acquire the status of necessary
laws. The first stage, where we simply record the
“phenomena” described by Kepler's “rules”
(as mere “appearances”: note 35 above), corresponds
to the category of possibility. The second stage, where we say
that we here have instances of “true” (as opposed to merely
“apparent”) rotation by appealing to the law of inertia,
corresponds to the category of
actuality.[37]
In the third stage, finally, we apply
the equality of action and reaction to the true centripetal
accelerations correlated with such true rotations (note 37 above); and
all of them, in accordance with Kant's metaphysical
“dynamical theory of matter,” must now be taken as
extending universally to infinity from each attracting point (compare
notes 34 and 36 above). The result is the law of universal
gravitation, now seen as falling under the category of necessity.
In this way, Kant's reconstruction of Newton's
“deduction” of the law of universal gravitation from the
initial Keplerian “phenomena” provides a perfect
illustration of the three-step procedure, described in the Postulates
of Empirical Thought, by which a mere “empirical rule” is
transformed into a “necessary and universally valid”
objective
law.[38]

We have suggested that Kant's reconstruction of Newton's
“deduction from the phenomena” of the law of universal
gravitation in the Metaphysical Foundations of Natural Science
is inextricably entangled with his reinterpretation of the Newtonian
concepts of (absolute) space, time, and
motion.[39]
Indeed, Kant begins the
Metaphysical Foundations by defining matter as “the
movable in space”—and by introducing a distinction between
absolute and relative space which is clearly derived from Newton's
Scholium on space, time, and motion at the beginning of
the Principia (see note 37 above). In Newton's words
(Principia, 408–409): “Absolute space, of its own
nature without reference to anything external, always remains
homogeneous and immovable. Relative space is any movable measure or
dimension of this absolute space.” In Kant's words (4, 480; 15):
“Matter is the movable in space. That space
which is itself movable is called material, or also relative
space. That space in which all motion must finally be
thought (and which is therefore itself absolutely immovable) is called
pure, or also absolute space.”

It turns out, however, that Kant's own view, in sharp contrast
to Newton's, is that “absolute space is in itself
nothing and no object at all,” but signifies only an indefinite
process of considering ever more extended relative spaces (4, 481–482;
16–17). Moreover, when Kant returns to this issue in the Phenomenology
chapter (compare note 35 above), he states that “absolute space
is therefore not necessary as the concept of an actual object, but
only as an idea, which is to serve as the rule for considering all
motion and rest therein merely as relative” (4, 560;
99). Kant's procedure for deriving “true motions”
from “apparent motions” does not conceive true motions as
taking place in an infinite empty absolute space (as in Newton), but
views them as the product of an indefinitely extended process of
empirical determination taking place within experience itself:
we begin from our parochial perspective here on the surface of the
earth, proceed (in accordance with the argument of Book 3 of
Newton's Principia)
to the center of gravity of the solar system,
then proceed to the center of gravity of the Milky Way galaxy, and so
on ad infinitum.[40]

Similarly, it is a central theme of the Analogies of Experience in
the first Critique that “absolute
time”—“time itself” (B219), “time for
itself” (B225), or “time in itself” (B233)—is
no actual object of perception. Hence, the three “modes of
time” (duration, succession, and simultaneity) must all be
determined in and through perceptible features of the
appearances. Kant calls this procedure “time
determination” (more precisely, “the determination of the
existence of appearances in time”), and he sums up his view as
follows (A215/B262):

These, then, are the three analogies of experience. They are nothing
else but the principles for the determination of the existence of
appearances in time with respect to all of its three modes, the
relation to time itself as a magnitude (the magnitude of existence,
i.e., duration), the relation in time as a series (successively), and
finally [the relation] in time as a totality of all existence
(simultaneously). This unity of time determination is thoroughly
dynamical; that is, time is not viewed as that in which experience
immediately determines the place of an existent, which is impossible,
because absolute time is no object of perception by means of which
appearances could be bound together; rather, the rule of the
understanding, by means of which alone the existence of the
appearances can acquire synthetic unity with respect to temporal
relations, determines for each [appearance] its position in time, and
thus [determines this] a priori and valid for each and every
time.

For Kant, therefore, the temporal relations of duration, succession,
and simultaneity cannot be viewed as pre-existing, as it were, in an
absolute time subsisting prior to and independently of the procedures
of our pure understanding for determining these relations within the
appearances themselves. On the contrary, temporal relations as
such are the products of an empirical construction whereby we
objectively determine the appearances as objects of a unified
experience by means of the a priori principles of the Analogies.
Thus, just as Kant does not view the determination of true motions from
apparent motions as taking place within an infinite empty absolute
space, he also rejects Newtonian absolute time and replaces it, too,
with a process of empirical determination taking place within
experience itself.

Indeed, there is an intimate relationship between these two
procedures for empirical determination—of time and of motion,
respectively. At the very beginning of his famous Scholium Newton
distinguishes between “true” and merely
“apparent” time (Principia, 408):
“Absolute, true, and mathematical time, in and of itself and of
its own nature, without reference to anything external, flows uniformly
and by another name is called duration. Relative, apparent, and
common time is any sensible measure (whether accurate or nonuniform) of
duration by means of motion: such a measure—for example, an hour,
a day, a month, a year—is commonly used instead of true
time.” Then, several pages later, Newton illustrates the
difference between “absolute” and “relative”
time with reference to the celestial motions studied in astronomy
(Principia, 410):

In astronomy, absolute time is
distinguished from relative time by the equation of common time.
For natural days, which are commonly considered equal for the purpose
of measuring time, are actually unequal. Astronomers correct this
inequality in order to measure celestial motions on the basis of a
truer time. It is possible that there is no uniform motion by
which time may have an accurate measure. All motions can be
accelerated and retarded, but the flow of absolute time cannot be
changed. The duration or perseverance of the existence of things
is the same, whether their motions are rapid or slow or null;
accordingly, duration is rightly distinguished from its sensible
measures and is gathered from them by means of an astronomical
equation.

Newton is here referring to the standard astronomical procedure,
already well-understood in ancient astronomy, whereby we correct the
ordinary measure of time in terms of days, months, and years so as to
obtain “sidereal” or mean solar time based on the motions
of the sun relative to both the earth and the fixed
stars.[41]

In the Refutation of Idealism added to the second edition of the
Critique Kant argues that all empirical determination of
time—including determination of the temporal relations among
one's own inner states—ultimately depends on the perception
of outer things, and, in particular, on the perception of motion in
space (B277–278):

All empirical employment of our cognitive faculties in the
determination of time fully agrees with this. It is not only that we
can undertake all time determination only by the change of external
relations (motion) in relation to the permanent in space (e.g., motion
of the sun with respect to objects on the earth), but we also have
nothing at all permanent, which could underlie the concept of a
substance, as intuition, except merely matter, and even this
permanence is not derived from outer experience, but is rather
presupposed a priori as necessary condition of all time determination,
and thus also [of] the determination of inner sense with respect to
our own existence by means of the existence of outer
things.

In emphasizing that only matter can instantiate the concept
of substance here, Kant is alluding to the way in which the
conservation of the total quantity of matter, in the Metaphysical
Foundations, realizes the (transcendental) principle of the
conservation of
substance.[42]
Moreover, Kant's language at
B277–278 (we “undertake [vornehmen]” time
determination by observing “motion of the sun with respect to
objects on the earth”) thereby suggests a progressive empirical
procedure in which we begin with our perspective here on earth, measure
the duration of time by the apparent motion of the sun, and then
proceed to correct this measure in light of our evolving
astronomical
knowledge.[43]

Yet for Kant, unlike Newton, this need for correction is not an
indication of a pre-existing absolute time subsisting prior to and
independently of our empirical procedures for determining temporal
magnitudes from observable motions. It rather implies that
empirically observable motions must be subject to a priori principles
of the understanding (a priori rules of time determination) in order to
count as fully objective experience within a unified, temporally
determinate objective world. Applying the relevant principles of
the understanding—the Analogies of Experience—therefore
results in a sequence of successive corrections or refinements of our
ordinary temporal experience, as the observable motions are
progressively embedded within an increasingly precise and refined
conception of temporality itself.

In the Metaphysical Foundations, in particular, Kant
articulates a specific realization of the Analogies of Experience in
terms of the Newtonian theory of universal gravitation.
Kant's three “laws of mechanics” (a version of the
Newtonian laws of motion: compare notes 12 and 31 above)
correspond to the three principles of the Analogies; the categories of
substance, causality, and community are realized by the system of
Newtonian massive bodies interacting with one another in the context
of what Newton, in Book III of the Principia, calls the
System of the World. The category of substance, that is, is realized
by the conservation of the total quantity of matter (mass) in all
interactions involving these bodies (compare note 42 above, together
with the sentence to which it is appended); the category of causality
is realized by the gravitational forces through which these
interactions take place (in accordance with the law of inertia); and
the category of community is realized by the circumstances that
precisely these forces are everywhere mutually equal and opposite. The
temporal relation of duration is thereby realized by the progressive
empirical procedure by which we successively correct our ordinary
measure of time in light of our evolving astronomical knowledge
(compare note 43 above, together with the sentence to which it is
appended).[44]
The temporal relation of
succession is realized by the deterministic evolution of the motions of
the bodies (masses) in question described by the law of universal
gravitation (according to which every later state of the system is
uniquely determined by its earlier
states).[45]
The temporal relation of simultaneity,
finally, is realized by the circumstance that gravitational forces
instantaneously connect each body in the system with all
other
bodies.[46]
It is in precisely this sense
that the procedure of time determination Kant describes in the
Analogies is intended to replace Newtonian absolute time.

We have now arrived at the most fundamental divergence between Kant
and Hume concerning causation and induction. For Hume, the order
of time is empirically given by the sequence of impressions and ideas
(and associations among them) which in fact happen to appear before the
mind. As Kant explains in the Second Analogy, however, such a
sequence, from his point of view, is “merely something
subjective, and determines no object, and can therefore in no
way count as cognition of any object at all (not even in the
appearance)” (A195/B240). For Kant, it is only the a priori
concept of causality (requiring a necessary rule of connection between
preceding and succeeding events) which can then transform a merely
subjective temporal sequence into an objective one (ibid.):

If we thus experience that something happens, then we always
presuppose thereby that something precedes on which it follows in
accordance with a rule. For otherwise I would not say of the object
that it follows, because the mere sequence in my apprehension, if it
is not determined by means of a rule in relation to something
preceding, justifies no sequence in the object. Therefore, it is
always in reference to a rule, in accordance with which the
appearances in their sequence (i.e., as they happen) are determined
through the previous state, that I make my subjective synthesis (of
apprehension) objective, and, it is solely under this presupposition
that even the experience of something happening is
possible.

It is for precisely this reason, Kant concludes, that mere induction
alone cannot be the ground for objective causal connections—which
presuppose both strict universality and necessity, and therefore must
be grounded on a priori concepts and principles of the pure
understanding (A195–196/B240–241):

It seems, to be sure, that this contradicts all remarks that have
always been made concerning the course of the employment of our
understanding, according to which we have only been first guided by
the perception and comparison of many concurring sequences of events
following on certain appearances to discover a rule, in accordance
with which certain events always follow on certain appearances, and we
have thereby been first prompted to make for ourselves the concept of
cause. On such a basis this concept would be merely empirical, and the
rule it supplies, that everything that happens has a cause, would be
just as contingent as experience itself: its universality and
necessity would then be only feigned and would have no true universal
validity, because they would not be grounded a priori but only on
induction.

For Kant, the concept of cause cannot possibly arise from a mere
repetition of resembling constant conjunctions (“concurring
sequences of events following on certain appearances”) producing
a merely subjective
custom.[47]
The procedure by which we apply the concept of cause to experience
cannot be merely inductive in the Humean sense; it must rather involve
a priori rules of the understanding through which we progressively
determine the objective causal relations between appearances—and
thereby determine the objective order of succession in time
itself.[48]

Kant thus has a completely different perspective from Hume's
concerning the uniformity of nature. For Hume, the principle of
uniformity is a supposition implicit in all of our inductive inferences
leading to the formulation of laws of nature. If this principle
itself had a foundation in the understanding (in either a priori or a
posteriori “reasoning”), then so would our inductive
inferences from observed constant conjunctions to so far unobserved
events. Yet the supposition in question—“that
instances, of which we have had no experience, must resemble those, of
which we have had experience, and that the course of nature continues
always uniformly the same” (T 1.3.6.4; SBN 89)—cannot
itself be justified by either demonstrative or inductive
reasoning. In the former case it would have to be
self-contradictory to imagine that the course of nature is not
sufficiently uniform; in the latter the attempted justification would
be viciously circular. The principle of uniformity, however, is
firmly based in custom or habit, as a universal principle of the human
mind, and it is also the foundation for the Newtonian inductive
method—including Hume's own inductive science of the human
mind. Although the principle thus has normative force in all our
reasoning concerning matters of fact in both science and common life,
it cannot ultimately legitimate the attribution of objective necessity
to our inductively established laws of
nature.[49]

Kant, in our view, is attempting to provide precisely such a grounding
of objective necessity by means of the general principle of the
Analogies of Experience (B218): “Experience is possible only by
means of the representation of a necessary connection of
perceptions.” More specifically, the Analogies of Experience
provide an a priori conception of the unity and uniformity of
experience playing the role, for Kant, of Hume's principle of the
uniformity of nature. According to the Analogies we know a priori that
nature in general must consist of interacting substances in space and
time governed by universally valid and necessary causal laws
determining the temporal relations (of duration, succession, and
simultaneity) among all empirical events, and this articulated a
priori conception of nature in general amounts to the knowledge that
nature is, in fact, sufficiently
uniform.[50]

We can only have objective experience of particular events, for
Kant, in so far as we simultaneously construct particular causal
relations among them step by step, and this is only possible, in turn,
in so far as we presuppose that they are one and all parts of a unified
and uniform experience of nature in space and time governed by the
Analogies of Experience (together with the other principles of pure
understanding). Moreover, since particular causal relations, for
Kant, necessarily involve causal laws, all of our inferences from
particular perceptions to universal causal laws of nature are grounded
in synthetic a priori principles of pure understanding providing a
synthetic a priori conception of the unity and uniformity of nature in
general. Hume was correct, therefore, that the principle of the
uniformity of nature governs all of our inductive causal inferences;
and he was also correct that this principle is not and cannot be
analytic a priori. What Hume did not see, from
Kant's point of view, is that the merely comparative universality
of inductive generalization can indeed be overcome by transforming
initially merely subjective “empirical rules” into truly
objective and necessary “universal laws” in accordance with
synthetic but still a priori principles of the unity of nature
in
general.[51]

Kant

Citations from Kant's works, except for the Critique of
Pure Reason, are by volume and page numbers of the Akademie
edition of Kant's gesammelte Schriften (Berlin,
1902—); the Critique of Pure Reason is cited by the
standard A and B pagination of the first (1781) and second (1787)
editions respectively. Although all translations from
Kant's writings are our own, we follow the reference to the
Akademie edition (except in the case of the Critique of Pure
Reason) with references to the translations in the now standard
Cambridge Edition of the Works of Immanuel Kant, as follows:

Theoretical Philosophy, 1755–1770, translated and
edited by David Walford, in collaboration with Ralf Meerbote
(Cambridge: Cambridge University Press, 1992). This volume contains
translations of Kant's pre-critical writings, including Attempt to
Introduce the Concept of Negative Magnitudes into Philosophy
(1763) and Dreams of a Spirit-Seer Explained by Dreams of
Metaphysics (1766).

Hume

Citations from Hume's A Treatise of Human Nature
(abbreviated as T) are from the David Fate Norton and Mary J. Norton
edition (New York: Oxford University Press, 2000), and thus include
book, part, section, and paragraph numbers; we also add the
corresponding page numbers in the L. A. Selby-Bigge second edition
(abbreviated as SBN), with revised text and notes by P. H. Nidditch
(Oxford: Oxford University Press, 1978).

Citations from Hume's An Enquiry concerning Human
Understanding (abbreviated as EHU) are from the Tom L. Beauchamp
edition (New York: Oxford University Press, 1999), and thus include
section and paragraph numbers; we also add the corresponding page
numbers in Enquiries concerning Human Understanding and concerning
the Principles of Morals, edited by L. A. Selby-Bigge, third
edition (abbreviated as SBN), with revised text and notes by P. H.
Nidditch (Oxford: Oxford University Press, 1975).

Locke

Citations from Locke's An Essay concerning Human
Understanding are from the Peter H. Nidditch edition (Oxford:
Oxford University Press, 1975), and include the Roman numerals of the
book and chapter, followed by the Arabic numeral of the
section.

Newton

Citations from Newton's Principia are to The
Principia: Mathematical Principles of Natural Philosophy,
translated and edited by I. Bernard Cohen and Anne Whitman, assisted by
Julia Budenz (Berkeley and Los Angeles: University of California Press,
1999), and are given in the form (Principia, page
numbers).

Citations from Newton's Opticks are to Opticks:
or A Treatise of the Reflections, Refractions, Inflections &
Colours of Light, based on the fourth edition, London 1730 (New
York: Dover, 1979), and are given in the form (Opticks, page
numbers).

The relevant secondary literature is vast. We confine
ourselves to English-language literature and, more specifically, to the
works cited in the main text. These works can be consulted, in turn, for
extensive references to other secondary literature.